F(x)=2x^2-25x+63

Solution for F(x)=2x^2-25x+63 equation:

(F)=2F^2-25F+63

We move all terms to the left:

(F)-(2F^2-25F+63)=0

We get rid of parentheses

-2F^2+F+25F-63=0

We add all the numbers together, and all the variables

-2F^2+26F-63=0

a = -2; b = 26; c = -63;
Δ = b2-4ac
Δ = 262-4·(-2)·(-63)
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{43}}{2*-2}=\frac{-26-2\sqrt{43}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{43}}{2*-2}=\frac{-26+2\sqrt{43}}{-4}
$